# Continuous-time vs discrete time identification?

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Joonas on 21 Nov 2015
Answered: Simone Pirrera on 19 Oct 2021
Hi,
I have a real plant that I'm sampling with 0.001 interval. For this reason all the measurement data in my Matlab are vectors that include data from every 1ms.
I have also constructed a state-space model for my real plant and I want to do greybox-modelling and thus identify some parameters of my real plant by using the measurement data.
I'm wondering now, should I do the parameter identification for a continuous-time state-space model of the plant, or for a discrete state-space model (discretized with 1ms sample time)? The real world is continuous, but the measurements from the plant are "discrete" as I have them only with 1ms interval. Thus, which is better, to use the measurement data to identify parameters for a continuous or discrete time state-space model?
Additionally, I do a idgrey model of my state-space model. Should I construct this idgrey model based on continuous-time model of the plant, or discretized model of the plant? The discrete-time idgrey model needs the "sampletime Ts" as input in order to produce the idgray object. Does the idgray-function discretize the model with the given sampletime and return the discretized grey-box model? Or is the "Ts" only used for metadata that is included into the idgrey object's data?
Thanks for any ideas for declaring this.
Cheers, Joonas

Simone Pirrera on 19 Oct 2021
Grey-box identification problem can be posed both in continuous and discrete-time. Depends on the physics of your system: most commonly plants are described as differential equations and therefore you have continuous-time models.
I can suggest you to read this article for a nice grey-box identification procedure that applies both to DT and CT models
O. Prot and G. Mercère, "Combining Linear Algebra and Numerical Optimization for Gray-Box Affine State-Space Model Identification," in IEEE Transactions on Automatic Control, vol. 65, no. 8, pp. 3272-3285, Aug. 2020, doi: 10.1109/TAC.2019.2942567.